130 Equivalence and Noninferiority Tests
–1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.0 0.2
0.0
0.2
0.4
0.6
0.8
1.0
Delta
Power
Test 2.1, R: power curve.
Test 2.2 Comparison of Two Means—Two Independent
Samples, Fixed Δ Paradigm (One-Sided)
Input parameters:
D0 = maximum desirable difference between means
mu1 = prior estimate of mean for group 1
n = sample size per group
SAS code:
libname stuff 'H:\Personal Data\Equivalence & Noninferiority\
Programs & Output';
data calc;
set stuff.d20120803_test_2_2_two_means;
mu2 = mu1 - Da;
delta = (D0 - Da)/sigma;
nc = sqrt(n/2) * delta;
tcrit = tinv(0.05,2*n-2);
power = 1 - probt(tcrit,2*n-2,nc);/* Pr{T' > = tcrit} */
run;
131Computer Code—Power Curves
proc print data = calc;/*dataset calc has columns n muL muA
sigma delta nc power */
run;
The SAS System 13:57 Friday, August 3, 2012 2
Obs n mu1 D0 Da sigma mu2 delta nc tcrit power
1 13 100 5 10.00 3.5 90.00 -1.42857 -3.64216 -1.71088 0.02925
2 13 100 5 9.75 3.5 90.25 -1.35714 -3.46005 -1.71088 0.04315
3 13 100 5 9.50 3.5 90.50 -1.28571 -3.27794 -1.71088 0.06195
4 13 100 5 9.25 3.5 90.75 -1.21429 -3.09583 -1.71088 0.08662
5 13 100 5 9.00 3.5 91.00 -1.14286 -2.91373 -1.71088 0.11797
6 13 100 5 8.75 3.5 91.25 -1.07143 -2.73162 -1.71088 0.15661
7 13 100 5 8.50 3.5 91.50 -1.00000 -2.54951 -1.71088 0.20278
8 13 100 5 8.25 3.5 91.75 -0.92857 -2.36740 -1.71088 0.25624
9 13 100 5 8.00 3.5 92.00 -0.85714 -2.18529 -1.71088 0.31626
10 13 100 5 7.75 3.5 92.25 -0.78571 -2.00319 -1.71088 0.38156
11 13 100 5 7.50 3.5 92.50 -0.71429 -1.82108 -1.71088 0.45044
12 13 100 5 7.25 3.5 92.75 -0.64286 -1.63897 -1.71088 0.52085
13 13 100 5 7.00 3.5 93.00 -0.57143 -1.45686 -1.71088 0.59063
14 13 100 5 6.75 3.5 93.25 -0.50000 -1.27475 -1.71088 0.65765
15 13 100 5 6.50 3.5 93.50 -0.42857 -1.09265 -1.71088 0.72004
16 13 100 5 6.25 3.5 93.75 -0.35714 -0.91054 -1.71088 0.77634
17 13 100 5 6.00 3.5 94.00 -0.28571 -0.72843 -1.71088 0.82558
18 13 100 5 5.75 3.5 94.25 -0.21429 -0.54632 -1.71088 0.86732
19 13 100 5 5.50 3.5 94.50 -0.14286 -0.36422 -1.71088 0.90161
20 13 100 5 5.25 3.5 94.75 -0.07143 -0.18211 -1.71088 0.92892
21 13 100 5 5.00 3.5 95.00 0.00000 0.00000 -1.71088 0.95000
132 Equivalence and Noninferiority Tests
JMP Data Table and formulas:
Power for Test 2.2, JMP screen.
R:
> df1 <- read.table("H:\\Personal Data\\Equivalence &
Noninferiority\\Programs & Output\\d20120803_test_2_2_two_
means.csv",header = TRUE,sep = ",")
> df1
n mu1 D0 Da sigma
1 13 100 5 10.00 3.5
2 13 100 5 9.75 3.5
3 13 100 5 9.50 3.5
4 13 100 5 9.25 3.5
5 13 100 5 9.00 3.5
6 13 100 5 8.75 3.5
7 13 100 5 8.50 3.5
8 13 100 5 8.25 3.5
9 13 100 5 8.00 3.5
10 13 100 5 7.75 3.5
11 13 100 5 7.50 3.5
12 13 100 5 7.25 3.5
133Computer Code—Power Curves
13 13 100 5 7.00 3.5
14 13 100 5 6.75 3.5
15 13 100 5 6.50 3.5
16 13 100 5 6.25 3.5
17 13 100 5 6.00 3.5
18 13 100 5 5.75 3.5
19 13 100 5 5.50 3.5
20 13 100 5 5.25 3.5
21 13 100 5 5.00 3.5
> mu2 <- df1$mu1 - df1$Da
> delsig <- (df1$D0 - df1$Da)/df1$sigma
> nc <- delsig*sqrt(df1$n/2)
> tcrit <- qt(.05,2*df1$n-2)
> power <- 1 - pt(tcrit,2*df1$n-2,nc)
> power
[1] 0.02925394 0.04315103 0.06195378 0.08661506 0.11796964
0.15661283
[7] 0.20277933 0.25624291 0.31625815 0.38156107 0.45043685
0.52085077
[13] 0.59062639 0.65764531 0.72003815 0.77633847 0.82557882
0.86731959
[19] 0.90161406 0.92892317 0.95000000
> plot(delsig,power)
–1.4 –1.2 –1.0 –0.8 –0.6 –0.4 –0.2 0.0
0.0
0.2
0.4
0.6
0.8
Delsig
Power
Test 2.2, R: power curve.
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